2022/12/16 by Alain Couvreur, Couvreur, Alain
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2212.08713
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates <1/2 there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank can be corrected. Moreover, the corresponding family of decodable codes includes Gabidulin codes of rate <1/2. Second, for rates >1/2, we propose a decoder for Gabidulin codes correcting symmetric errors of rank up to n-k. The two mentioned decoders are deterministic and worst case.